Differential Geometry Courses and Certifications

Utrecht Geometry Centre

Geometry, Mechanics, and Control - Young Researchers Workshop

Explore advanced topics in differential geometry, optimal control theory, and mathematical physics through expert lectures on Pontryagin principles, contact manifolds, and Hamiltonian systems.

• YouTube
• 9 hours 47 minutes
• Self-Paced
• Free Video

Tobias Osborne

General Relativity

Master Einstein's theory through manifolds, tensors, curvature, field equations, and solutions including Schwarzschild metrics, gravitational waves, and cosmological models.

• YouTube
• 21 hours 40 minutes
• Self-Paced
• Free Video

Math with Professor V

Calculus 3 Quick Tips - Double Integrals, Surface Integrals, and Lagrange Multipliers

Master essential Calculus 3 techniques including double integrals, surface integrals, Lagrange multipliers, polar coordinates, and order of integration through focused problem-solving sessions.

• YouTube
• 2 hours 58 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

Advanced Topics in Mathematical Gauge Theory - Higgs Bundles

Delve into advanced mathematical gauge theory and Higgs bundles through expert lectures covering sophisticated theoretical frameworks and their geometric applications.

• YouTube
• 4 hours 11 minutes
• Self-Paced
• Free Video

IAS | PCMI Park City Mathematics Institute

Introduction to Gauge Theory

Dive into gauge theory fundamentals through comprehensive mathematical lectures covering connections, curvature, and applications in modern geometry and physics.

• YouTube
• 4 hours 46 minutes
• Self-Paced
• Free Video

Michael Penn

Calculus of Vector Valued Functions

Master derivatives, integrals, arc length, and curvature of vector-valued functions through detailed examples and explore curves in 3D space with associated vectors and planes.

• YouTube
• 1 hour 35 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Discrete Subgroups of Lie Groups - Dynamics, Actions, Rigidity

Explore advanced mathematical concepts in discrete subgroups of Lie groups through expert-led mini-courses covering dynamics, rigidity theory, and geometric applications.

• YouTube
• 1 day 15 hours
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Mathematics on the Crossroad of Centuries

Explore cutting-edge mathematics bridging algebra, geometry, topology, and physics through expert lectures honoring Maxim Kontsevich's groundbreaking contributions.

• YouTube
• 20 hours 55 minutes
• Self-Paced
• Free Video

Institut des Hautes Etudes Scientifiques (IHES)

Workshop on Quantum Geometry

Explore advanced quantum geometry through expert lectures on Gromov-Witten theory, Donaldson-Thomas invariants, integrable systems, and spectral curve quantization from leading researchers.

• YouTube
• 14 hours 45 minutes
• Self-Paced
• Free Video

Mathemaniac

The Story of "dx" - Essence of Differential Forms #1

Discover the fascinating history behind "dx" and how differential forms revolutionized mathematics and physics through algebraic computations and geometric insights.

• YouTube
• 16 minutes
• Self-Paced
• Free Video

International Centre for Theoretical Sciences

Physics of Biological Membranes

1 rating

Explore the physics of biological membranes, covering lipid bilayers, surface energy, curvature, fluctuations, and non-equilibrium processes in this comprehensive lecture on membrane biophysics.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

Topology Shapes Dynamics of Higher-order Networks

Exploring how higher-order network interactions influence non-linear dynamics, synchronization, and percolation in complex systems like brain networks and climate patterns.

• YouTube
• 56 minutes
• Self-Paced
• Free Video

Multidimensional Analysis and Geometry - Introduction to the Derivative in Higher Dimensions - Lecture 1

Explore the derivative in higher dimensions, extending single-variable concepts to multidimensional functions and introducing the derivative as a linear map for best approximation.

• YouTube
• 53 minutes
• Self-Paced
• Free Video

Lie Groups - Introduction to Lie Groups

Discover Lie Groups through examples in this Oxford undergraduate lecture, exploring their applications in analysis, geometry, and physics from foundational concepts.

• YouTube
• 50 minutes
• Self-Paced
• Free Video

Insights into Mathematics

The Triple Spread Formula, Circumcircles and Curvature - Rational Geometry Math Foundations

Explores the Triple spread formula in Rational Trigonometry, relating it to circumcircles and curvature. Connects projective geometry with one and two-dimensional geometries through core circles and quadratic curvature.

• YouTube
• 24 minutes
• Self-Paced
• Free Video